Theory of Half-Metal/Superconductor Heterostructures

We investigate the Josephson coupling between two singlet superconductors separated by a half-metallic magnet. The mechanism behind the coupling is provided by the rotation of the quasiparticle spin in the superconductor during reflection events at the interface with the half metal. Spin rotation induces triplet correlations in the superconductor which, in the presence of surface spin-flip scattering, results in an indirect Josephson effect between the superconductors. We present a theory appropriate for studying this phenomenon and calculate physical properties for a superconductor/half-metal/superconductor heterostructure.

Figure 1

Scattering geometry illustrating the scattering channels and the corresponding transfer amplitudes for the model discussed in the text.

Figure 2

Self-consistent order parameter and triplet correlations in an S/HM/S heterostructure for a zero junction and a $\pi$ junction. The relative signs of the pairing correlations in the $s$-wave singlet and three $p$-wave triplet channels are indicated. A zero junction for the singlet order parameter leads to a relative phase difference of $\pi$ for the triplet correlations, and vice versa. The calculations are for temperature $T=0.05T_c$, and for ${\tau }_{\downarrow \uparrow }/{\tau }_{\uparrow \uparrow }=0.7$.

Figure 3

Critical Josephson current density as a function of temperature for an S/HM/S heterostructure. The two curves are for ${\tau }_{\downarrow \uparrow }/{\tau }_{\uparrow \uparrow }=0.1$ (dashed line) and ${\tau }_{\downarrow \uparrow }/{\tau }_{\uparrow \uparrow }=0.7$ (full line). The inset shows the current-phase relationships for ${\tau }_{\downarrow \uparrow }/{\tau }_{\uparrow \uparrow }=0.7$ for temperatures $T/T_c=0.05$ (dashed line), 0.2, 0.3, 0.4, and 0.5 (full lines from bottom to top). The unit is the Landau critical current density $J_L=e{v}_f{N}_f{\Delta }_0$, with the zero temperature bulk superconducting gap ${\Delta }_0=1.76T_c$.

Figure 4

Density of states at $T=0.05T_c$ for quasiparticles with normal impact at the half-metallic side of the left interface ($x=-L_H$), for (a) spin-flip rate ${\tau }_{\downarrow \uparrow }/{\tau }_{\uparrow \uparrow }=0.1$ and phase difference $\varphi =0.5\pi$, and (b) ${\tau }_{\downarrow \uparrow }/{\tau }_{\uparrow \uparrow }=0.7$ and $\varphi =0.2\pi$. The corresponding Josephson currents are close to the critical values. Shown are both states carrying current in positive (full lines) and negative directions (dashed lines).